Chernobyl in America
Could Chernobyl happen in America today? No. Thank you for reading.
To make this post a bit more engaging however, I will detail how I came to that conclusion. I am a nuclear chemist, and lover of clean energy— and nuclear is the best solution to clean energy that we have today. Why nuclear energy is the solution to clean energy is a topic for another post however. Today we will focus on why Chernobyl could not happen in America today.
A Simple Understanding of the Fission Mathematical Model.
Before we even get into this topic, you must understand the nuclear chain reaction to some small degree. The inherent power of nuclear fission is its exponential energy output. It works just like investment math you may have learned before.
OUTPUT = INPUT * ( 1 + %INTEREST ) ^ ( TIME / COMPOUNDING PERIOD*)
*We will come back to this asterisk later
So for example if you invest $10,000 at 10% interest over 5 years, and your investment compounds annually, you would earn:
$10,000 * ( 1 + 10% ) ^ ( 5 years / 1 year ) = $16,105.1
The inherent power in this mathematical model comes from the exponential chain: $10,000 at 10% yields $11,000, but then $11,000 at 10% yields $12,100— an additional $100 in the second iteration. So the same model that makes investors so wealthy makes nuclear reactors so powerful.
The Controllability of Nuclear Reactors
The Neutron Lifecycle is modeled by the same exact mathematical formula, but there is a bit of a twist. Neutrons born from a fission event are called “prompt”. These neutrons undergo the entire fission chain reaction in the scale of tens of microseconds, that is 0.00001 seconds.
Now looking back, the chain reaction time represents the same variable in the investment formula that the compounding period does. What does that mean? Well lets try the same exercise as before, but instead of starting with $10,000, lets start with 1 tiny prompt neutron compounding over 1 second at a 0.2% return rate.
1 Neutron * ( 1 + 0.2% ) ^ ( 1 second / 0.00001 seconds ) = 5.91E+86
What is this saying? If you start with a 1 prompt neutron at a 0.2% “interest”, by the end of one second you would have multiplied that neutron by a number that is larger than the number scientists use to estimate the value of all of the atoms in the observable universe. Obviously this mathematical model breaks down at such extreme scales but its important to understand this concept. This is prompt criticality, the condition in which a reactor is uncontrollable.
So reactor control requires a sufficiently slow compounding period, or generation time. The generation time can be either longer or shorter depending on the condition of the reactor. A different type of neutron called delayed neutrons make the reactor controllable. How you might ask? Well the specifics are a matter for another post, but essentially delayed neutrons change the average generation time from a matter of 0.00001 seconds to a much more controllable 1/10 of a second.
The Chernobyl Accident
The nuclear accident at Chernobyl directly resulted from the gross misconduct of reactor controls and a deadly error in design. The Chernobyl team violated safety procedures in a core with a positive void coefficient and graphite tipped control rods. What does this mean?
The team was attempting to perform testing, but did not understand the effects of poisons on the core. Thinking back to our earlier model— the percentage increase in neutrons relates to a concept called the effective multiplication factor, and poisons within the core reduce that factor.
Unbeknownst to the Soviets, poisons were present at the time of testing. To combat this the Chernobyl team withdrew control rods to a dangerous level to try to reach a required power level. These poisons did not last forever however and when they burned out reactor power began to increase.
Design Failures
Two dangerous design concepts led to the steam explosion at Chernobyl. The use of a positive void coefficient in reactor design, and the use of graphite materials on the tips of the control rods. A positive void coefficient essentially is a term that relates “percent neutron yield” to temperature. In cores with this design percent yield increases with moderator temperature. Essentially as the core gets hotter, it creates more power.
The issue here is simple, if the core gets hotter, it will create more power, and in turn more power means it will get hotter, and so on in a temperature feedback loop. When the poisons burned out the core started getting hotter. This devastating chain cycle could cause the destruction of the core, but virtually all reactors have an emergency back up protection “kill switch”. This “kill switch” called a SCRAM introduces our second design failure.
A reactor SCRAM plunges the control rods into the core by spring force at astonishing speed. This is to kill the chain reaction and make the reactor go subcritical. While most of the material of the RBMK reactor’s control rod lowered the “percent neutron yield” killing the chain reaction, the tips of the control rods were made from graphite, a material that increased the “percent neutron yield”.
When the failed testing required the operators at Chernobyl to use the SCRAM system, their “kill switch” actually ended up increasing reactor power, and the control rods became stuck due to steam pressure in a way such that the rods only made the core more powerful.
Finally we return to the concept of reactor controllability we discussed earlier. As we discussed, generation time could go up or down. In this disaster, it is believed that generation time reached the worst case scenario: prompt criticality. Much faster than you can blink the instantaneous power of the Chernobyl reactor would have been multiplied by a factor of thousands. This led to the steam explosion, which stopped the chain reaction, and subsequent disaster everyone knows of today.
So could this happen in America today?
No. It is illegal in America, and the EU for that matter, to license a nuclear reactor that operate based off of the positive void coefficient reactor design. Instead American reactors operate based off of a negative temperature coefficient. This means that if the core gets hotter, power decreases, making the core get colder, making power go up. These oscillations continue like a sin wave until reactor power reaches a stable condition.
This is not to say that a nuclear accident is impossible in America. The failures at Three Mile Island prove that even American operators must remain vigilant. But the accident that happened at Chernobyl could not happen in America.
Post by Zachary B. Zastrow
